Question

Given no other information, Calculate the age of a sample that has only 76% of its original ^​14 ​C.

Answer 1

Solution :-

half life of the 14C is 5730 years

so the rate constant of the decay process is calculated as follows

rate constant K = 0.693 / half life

                          = 0.693 / 5730 years

                         = 0.000121 yr-1

now lets calculate the time takes to decay sample from 100 % to 76 %

ln([A]t/[A]o ) = - K*t

ln[76/100] = -0.000121 yr-1 * t

-0.27443 = -0.000121 yr-1 * t

-0.27443 / -0.000121 yr-1 = t

2268 year = t

so the age of the sample is 2268 years.